Theory: Gradient with respect to particle i

Asalih3d

Hey guys

I've been trying to understand a thing which is explained a bit in this answer:

https://physics.stackexchange.com/questions/69100/meaning-of-gradient-with-respect-to-coordinates-of-particle-in-sph?fbclid=IwAR3UPtXFjbVx1mnxrK25lPXfuux4cFJG2DSTXHzkBsAb1FQcwlB1THDoafE

I understand everything up to:




1) I don't understand how he goes from nabla W to W' and an r hat vector.

2) Also I don't understand what is the difference between nabla and ' in this case. I understand nabla is spatial derivative with respect to xyz, while ' might be with respect to q = r/h ?

3) What does the hat vector really mean? Is it just that:

r = (x,y,z) ----> r_hat = (-z,y,x)

But as far as I know a lot of different r_hat can exist in 3d?

I hope someone would take a bit of time explaining this concept to me or maybe guide me to another explenation of how to understand gradient with respect to i computionally.

Kind regards

sph_tudelft_nl

Why would you not contact the OP (original poster) by placing a comment under his/her answer? They are the best people to explain intentions and notations. I guess that at least for some Stackoverflow community there is the possibility to have an extended conversation in a virtual chatroom as the need be. This does not address your concerns directly, but hopefully helps you find the answer you wish.